To determine the frequency of this oscillation from the graph, we need to first extract the period of the wave, which is the time it takes for one complete cycle of the oscillation.

Steps:

1. Period (T): The period is the time interval between two consecutive points where the wave repeats itself. Looking at the graph:

   • One cycle seems to start at $t = 0$ and completes around $t = 4$ seconds.
   • Thus, the period $T$ is 4 seconds.

2. Frequency (f): Frequency is the inverse of the period and is given by the formula: $f = \frac{1}{T}$ Substituting $T = 4$ seconds: $f = \frac{1}{4} = 0.25 \, \text{Hz}$

Answer:

The frequency of the oscillation is $0.25 \, \text{Hz}$.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. What is the relationship between frequency and period?
2. How would the graph look if the frequency increased?
3. What are the units of angular frequency, and how can you calculate it from the frequency?
4. How would you calculate the amplitude of this oscillation from the graph?
5. What is the significance of the phase shift in oscillatory motion?

Tip: When analyzing oscillatory motion, always check both the period and amplitude to fully understand the wave's behavior.